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I wrote an introductory note about elliptic curves and modular functions. At the begining it was supposed to be just an introduction to an article about very cool proof of Siegel. However, in the meantime I broke my finger (quite severely, bone is in many pieces…) and it’s still hard for me to use keyboard.

Accordingly, first few paragraphs aren’t very relevant, as they describe my admiration of Siegel’s proof.

I use Unicode for mathematical notation. Enjoy :-)

I continue to read Sheldon Katz’s book “Enumerative Geometry and String Theory”. Here’s question I posted on sci.physics. If you have any answer, comment or ANYTHING, please (rather: I BEG YOU, CRYING ON THE FLOOR!!!) share them. It’s really hard to find someone who is mathematician and who’s interested enough in physics to answer even such simple questions… In my department there is only one more guy I didn’t yet ask (about what follows or some other physical questions) , but I don’t trust him – he was a physicist in his youth. Read the rest of this entry »

(I don’t think that being educated dummy is something bad – in fact, I consider myself to be one).

Around month ago, I gave here, at Warsaw University, a very introductory talk about Gromov-Witten invariants. It was aimed at students who hadn’t heard about this topic but who knew standard things from university course: cohomology, vector bundles, Chern classes, Poincare duality, etc. There were also some local wise men and they didn’t say I totally screw it up.

It was based on first 9 chapters of a Sheldon Katz’s fantastic book: “Enumerative geometry and string theory” . This is suberbly written, it starts at the level of highschool students and it ends… well I don’t actually know where it ends, because I still have some chapters to read, but it surely introduces Gromov-Witten invariants.

Accordingly, the book has actually one disadvantage: Katz tries to explain really all, even things like what topology is. So, in case You know at least *very *roughly things I mentioned above, You may want to read notes I prepared.

Everything is in “algebraic geoemtry framework” – so that it’s meaningful to speak about for example cubics in **P**** ^{2}**. When I write

**P**

**, I mean**

^{n}**C**

**P**

**. I use unicode for mathematical notation.**

^{n}Any kind of feedback is welcomed!

BTW, I just found out that Sheldon is actually a name, not surname. When I was writing the notes, I didn’t check it and so I write “Sheldon’s book” instead of “Katz’s book”. Sorry for that.

BTW2, There’s a new edition of a book “J-holomorphic curves and symplectic topology” by Dusa McDuff and Dietmar Salamon. It has about 5 000 000 pages (I know what I’ve seen. However, Amazon says it has 669). First edition had 200 and I could at least dream of understanding it someday. Life’s so damn cruel.

BTW3, WOW!!! Maxim Kontsevich comes to Warsaw next week!!!! Believe it or not, but in the last post I chose Kontsevich as a random Fields medalist! :-).

As I wrote earlier, I’m reading “The road to reality” (R2R) by Roger Penrose (RP). I want to share some thoughts about what I have already read:

1. The greatness of Euclid (and also Gauss, to some extent)

2. Uses of negative numbers in physics

Read the rest of this entry »

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